Webinar: Improving Mathematical Problem Solving in Grades 4 through 8

1. Webinar:Improving Mathematical Problem Solving in Grades 4 through 8 September 30, 2014

2. WebEx Instructions

3. WebEx instructions Attendees can provide non-verbal feedback to presenters utilizing the Feedback tool.

4. WebEx instructions Feedback options:

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6. WebEx instructions Attendees should utilize the “Q&A” feature to pose questions to the speaker, panelists, and/or host. The host will hold all questions directed toward the speaker or panelists until the end, when they will be answered during a Q&A session.

7. Welcome and Overview Lydotta Taylor, Ed.D. Research Alliance Lead, REL Appalachia

8. Regional Educational Laboratory (REL) Program • U.S. Department of Education, Institute of Education Sciences. • RELs provide regional support for: • Applied research and evaluation. • Technical support and information sharing to build capacity to use data for improved education outcomes.

9. REL Appalachia’s mission • Meet the applied research and technical support needs of Kentucky, Tennessee, Virginia, and West Virginia. • Bring evidence-based information to policymakers and practitioners: • Provide support for a more evidence-reliant education system. • Inform policy and practice for states, districts, schools, and other stakeholders. • Focus on high-priority, discrete issues and build a body of knowledge over time.

10. How we work: Research alliances • What is a research alliance? • A partnership between education stakeholders and REL Appalachia. • What is the purpose of a research alliance? • As partners, REL Appalachia and alliance members develop and carry out a research and analytic technical assistance agenda on priority topics. • Who are the education stakeholders in an alliance? • May include representatives from one or more schools, divisions, state education agencies, and other organizations (e.g., colleges and universities).

11. Goals of today’s webinar Understand the importance of incorporating mathematical problem solving in daily instruction. Learn about the links between the NCTM’s 5 process standards, the Common Core Standards for Mathematical Practices, and the Virginia Standards of Learning. Describe the research base for the standards and illustrate how they can be put into practice in the middle grades.

12. Connect with us! www.relappalachia.org @REL_Appalachia Lydotta Taylor Lydotta@levation.com

13. Improving Mathematical Problem Solving in Grades 4 through 8 John Woodward, Ph.D. Dean, School of Education University of Puget Sound

14. Why is problem solving important for today’s math classroom?

15. Why problem solving is important • Problem solving has tended to play a minor role in most math classes. • Independent seatwork. • Homework. • “End of chapter” problem sets. • Problem solving is one of the defining features of math instruction in successful countries. • Singapore makes problem solving central to its most recent curriculum. • Data, technology, and the world of work.

16. Links between the NCTM Process Strands, the CCSS Mathematical Practice Standards, and the Virginia Mathematics Standards of Learning

17. Links between NCTM, CCSS, and the Virginia SOLs National Council of Teachers of Mathematics (NCTM) Process Strands Common Core State Standards (CCSS) Virginia Mathematics Standards of Learning (SOL)

18. Making sense of different standards for problem solving

19. 5 strands with common titles

20. 5 strands with common titles Continued

21. 5 strands with common titles

22. Foundation for CCSS-M Mathematical Practice Standards • “These practices rest on important ‘processes and proficiencies’ with longstanding importance in mathematics education.” —Introduction to the CCSS Mathematical Practice Standards • The CCSS Mathematical Practice Standards draw from: • NCTM’s Process Strands. • National Research Council’s Adding It Up: Helping Children Learn Mathematics (2001). Sources: CCSS Mathematical Practice Standards, http://www.corestandards.org Adding It Up (2001), http://www.nap.edu

23. The 8 CCSS-M Mathematical Practice Standards • Make sense of problems and persevere in solving them. • Reason abstractly and quantitatively. • Construct viable arguments and critique the reasoning of others. • Model with mathematics. • Use appropriate tools strategically. • Attend to precision. • Look for and make use of structure. • Look for and express regularity in repeated reasoning.

24. Virginia SOL and CCSS Standards Continued

25. Virginia SOL and CCSS Standards

26. From research to application: Putting the standards into practice in the middle grades

27. What kind of empirical support for these practices? The Problem Solving Guide (PSG) Source: Woodward, J., Beckmann, S., Driscoll, M., Franke, M., Herzig, P., Jitendra, A., Koedinger, K. R., & Ogbuehi, P. (2012). Improving mathematical problem solving in grades 4 through 8: A practice guide. The RtI Guide (RtI) Source: Gersten, R., Beckmann, S., Clarke, B., Foegen, A., Marsh, L., Star, J. R., & Witzel, B. (2009). Assisting students struggling with mathematics: Response to Intervention (RtI) for elementary and middle schools.

28. PSG: Relevant recommendations and evidence

29. RtI: Relevant recommendations and evidence

30. Recommendations Continued

31. Recommendations Continued

32. Recommendations

33. Recommendations

34. Virginia SOL and CCSS Standards Example 1

35. PSG Recommendation 2 • Provide students with a list of prompts to help them monitor and reflect during the problem-solving process. • Model how to monitor and reflect on the problem-solving process. • Use student thinking about a problem to develop students’ ability to monitor and reflect.

36. PSG Recommendation 2 This is what we want teachers to AVOID: • Read the problem (and read it again). • Find a strategy (usually “make a drawing”). • Solve the problem. • Evaluate the problem.

37. PSG Recommendation 2 Instead, provide prompts or model questions: • What is the story in this problem about? • What is the problem asking? • What do I know about the problem so far? • What information is given to me? • How can this help me? • Which information in the problem is relevant? • Is this problem similar to problems I have previously solved? • Why do (or did) these steps work or not work?

38. Virginia SOL and CCSS Standards Example 2

39. RtI Recommendation 4 • Problem: “It is summer and my job is to weed the garden. Last Friday I counted 45 weeds in the garden. I didn’t do any work on the weekend. Now it is Wednesday, and there are 72 weeds in the garden. How many more weeds grew in the garden?” • Type of problem: Subtraction Compare Problem • Other types of subtraction problems: • Separate (“I had 10 balloons, and I gave 4 to my sister ...”) • Part-Part-Whole (“Sarah has 12 coins; 3 are nickels, 4 are dimes, the rest are pennies. How many …”)

40. Virginia SOL and CCSS Standards Example 3

41. PSG Recommendation 3, RtI Recommendation 5 Simple ratio and proportion problems are just that. Problem: “Apples are 3 for $2. How much would you pay for 12 apples?”

42. PSG Recommendation 3, RtI Recommendation 5 • Problem: “Apples are 5 for $2. How much would you pay for 9 apples?” It costs $3.60 for 9 apples.

43. Virginia SOL and CCSS Standards Example 4

44. PSG Recommendation 4 Problem: “Find the measure of angle x.”

45. PSG Recommendation 4

46. PSG Recommendation 4

47. PSG Recommendation 4

48. PSG Recommendation 4

49. PSG Recommendation 4

50. PSG Recommendation 4